The essay is correct, Some remarks are :
1. Try to give variables names different than those of already built in functions , like phase.
2.The random variables is scalar, instead use randn(size(n)), to generate a vector.
3.the function abs(U) computes the magnitude if U is complex, no need to square the result.
4.the defined SNR is correct only for real values signal, which is not in this case, for this example use real(sinusoid) instead.
5. You have to scale the fft result in order to obtain the correct power ( std(u)).
6. You can increase the number of points N for FFT computation as follows fft(u,N).
7. With low number of time samples, you can not detect both frequencies f1 and f2, you need larger number of samples, this is related to Heisenberg uncertainty principle in signal processing, as example for n=310, you can detect the frequencies.
clear all;close all;
f1=0.115; f2=0.135; n=0:310-1;
%PHASE=2*pi*rand();
w=0.1*randn(size(n));
u=real(exp(j*2*pi*f1*n))+real(exp(j*2*pi*f2*n))+w;
%Using FFT
N=600;
U=2*fft(u,N)/N;
fvals=(0:N-1)/N;
mag=abs(U);
subplot(1,2,1);plot(fvals,mag);
xlabel('Frenquency'); ylabel('P(f)'); title('Power spectrum by FFT method');
subplot(1,2,2);plot(fvals,10*log10(mag.^2));
xlabel('Frequency'); ylabel('P(f)'); title('Power spectrum by FFT method in dB');
